Nano-scale friction and wear of polymer coated with graphene

7 Background: Friction and wear of polymers at the nano scale is a challenging problem due to the 8 complex viscoelastic properties and structure. Using molecular-dynamics simulations, we investi9 gate how a graphene sheet on top of a semicrystalline polymer (PVA) affects the friction and wear. 10 Results: Our setup is meant to resemble an AFM experiment with a silicon tip. We have used two 11 different graphene sheets: an unstrained, flat sheet, and one that has been crumpled before being 12 deposited on the polymer. 13 Conclusion: The graphene protects the top layer of the polymer from wear and reduces the fric14 tion. The unstrained flat graphene is stiffer, and we find that it constrains the polymer chains and 15 reduces the indentation depth. 16


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Graphene is a two dimensional material that has remarkable properties, both electronic [1,2] and show that a transfer film of graphene on the polymer leads to lower friction. While to our knowl- 38 edge there have been no numerical studies of friction on graphene coated polymers, the graphene 39 polymer interface has been studied. Rissanou et al. [29,30] show that graphene has a strong ef-40 fect on the structure and dynamics of the polymer chains near the interface. In this work, we aim 41 to develop our understanding of the frictional behaviour of polymer coated with graphene by us-42 ing molecular dynamics simulations of a single sliding asperity at the nanoscale. We show that 43 graphene protects the polymer substrate from wear and identify the mechanism of this protection. 44 We show that crumpling of the graphene has an impact on the friction. In section we first describe 45 the simulation setup. Then we move on to discussing our simulations of depositing, indenting, and 46 sliding on the graphene in section . Finally, we draw some conclusions in section . 47 We simulate a slab of polyvinyl alcohol (PVA) coated with a single layer of graphene and a coun-49 terbody representing an AFM tip consisting of silicon. The simulations were peformed using 50 LAMMPS [31]. We use the same setup for the polymer as our previous work [25], which we sum-51 marise below.  For graphene, we use the potential developed by O'Connor et al [33] (AIREBO-M potential). It is 61 an empirical many-body potential that is directly implemented in LAMMPS.

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The interaction between the PVA and graphene is modelled using a Lennard-Jones 12-6 potential  depth potential, and 2 = 3 Å is the distance at which the potential is equal to zero.

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In our system, the tip and polymer are never in direct contact. They are always separated by 69 graphene. We therefore do not need to model their interactions, but to be sure that no extremely 70 unphysical events can occur, we have used the same potential as for the polymer-polymer interac-71 tion.

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The masses of the particles were chosen to be equal to 12.01 g/mol for the carbon atom of crystallized substrate structure, we cool down the sample using a Nosé-Hoover thermostat with a 90 linearly decreasing temperature, starting at 5000 K down to 220 K with a cooling rate of 75 K/ns.

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After this, the temperature is kept constant at 220 K for 4 ns. At this point, we remove the walls 92 and the direction as they are no longer needed.

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Graphene deposition 94 After the solidification of the semi-crystalline substrate, a layer of graphene is deposited on top. 95 We use two different graphene sheets in our simulations. The first one is a single flat sheet of 96 graphene that has the size of the box (Fig. 2a). The second one is also a single sheet, but the 97 graphene has been crumpled by being compressed along and directions by 10%, which leads 98 to wrinkles on the surface (Fig. 2b).

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In both cases, we deposited the graphene on the surface of the polymer substrate by placing the where the graphene atoms are fixed are located in strips along the direction, which is the sliding 108 direction, as far away as possible from the trajectory of the tip (Fig. 3).

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The FFM tip is rigid and consists of atoms arranged in an fcc lattice with a period of 5.43 Å, which 110 is the crystal structure of silicon. A semisphere is cut out from this material. The tip is placed  We calculate the surface roughness of the top polymer atoms. We first divide the box into bins of 122 size 0 in both and . Each bin is assigned the height of the atom with the highest position. We 123 6 finally compute the surface roughness as the root mean square height of a given area, 125 where A is the surface area and Z is the height of the particles on the surface.

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In addition to the shape, the structure of the polymer near the surface is affected by the graphene.

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In the case of the flat graphene, the particles of the polymer align in layers parallel to the surface, 140 as can be seen in Fig. 4b. In Figure b), the red flat region corresponds to a depth at which there is 141 a high density of polymers. A similar effect has been observed for other polymers as well [29,30].

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For the crumpled graphene, the structure of the polymer is not as strongly affected by the deposi-143 tion (Fig. 4c), though there is some sign of it.

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After the graphene is deposited, we add the AFM tip to our simulation and indent it into the sur-146 face. Figure   We have run a long indentation simulation with a load of 6.4nN to determine the penetration depth 153 after a long period of time (see Fig. 5). We only observe a slight increase in the depth between 1 ns 154 and 4 ns of around 1 Å. Thus, we consider the tip indented fully after 1ns.

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The indentation depth depends strongly on the load, as expected ( Fig. 6). At low normal force, the 156 tip with a higher radius penetrates deeper due to adhesion, which contributes significantly to the 157 effective load force by pulling the tip into the surface. At higher loads, the smaller tip penetrates 158 further, as it is subjected to larger external pressure. In the case of the crumpled graphene, we 159 see a larger indentation depth compare to the flat graphene (Fig. 8). The tip has more freedom to 160 sink inside the material when the graphene is crumpled (membrane buckling) than in a case of flat 161 graphene (stiff membrane).
162 Figure 7 shows the cross-section of the density under the tip at the end of the indentation process. 163 We can see regular lines of high density right below the graphene which indicate a local reorgan- Once the tip is sufficiently indented into the surface (after 1 ns), we start the sliding. Figure 10 169 shows the lateral force as a function of the displacement of the support in the case of the flat 170 graphene.

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To better highlight the influence of the tip radius, we average the frictional forces between the sup-172 port displacement 50 and 100 Å. We plot those results as a function of the normal load for two dif-173 ferent tip sizes (radius of 50 and 100 Å) in Fig. 11. We observe a regular stick-slip motion. The 174 distance between sticks corresponds to one lattice period of the graphene. 175 We observe in Fig. 10 that for the highest loads the frictional force increases during sliding. This 176 may be due to local frictional heating leading to a change in mechanical properties of the polymer 177 below the tip.

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In the case of the crumpled graphene (Fig. 12), the frictional curve is subject to more fluctuations.

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The calculation of the average frictional force taken between support displacements 50 and 100 Å 180 (Fig. 14) shows the strong impact of the flexibility of the graphene. Again, the higher indentation 181 depth of the tip leads to a stronger frictional force (2 to 3.5 times).

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We compare this to sliding without graphene. In a simulation with no graphene, a normal load of 183 51 nN, and a tip radius of 100 Å, we found that the tip moves deeply inside the substrate and the av-184 erage friction is above 90nN, almost an order of magnitude higher than with graphene. This clearly 185 shows that the graphene layer darstically reduces the friction.

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To observe the effect of sliding on the wear of the polymer material, we compare three simulations: 187 one without graphene, one with flat graphene, and one with crumpled graphene. All have a nor-188 mal load of 1 nN and a tip radius of 50 Å (Fig. 13). To improve the averaging by increasing the 189 total sliding distance, we increase the sliding speed by a factor 10 to 20 m/s. The displacement 190 vectors are recorded after 0.6 ns, meaning that the support has moved 120 Å. This is indicated by